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Scientific Computing

Numerical simulation of real-world phenomena provides fertile ground for building interdisciplinary relationships. The SCI Institute has a long tradition of building these relationships in a win-win fashion – a win for the theoretical and algorithmic development of numerical modeling and simulation techniques and a win for the discipline-specific science of interest. High-order and adaptive methods, uncertainty quantification, complexity analysis, and parallelization are just some of the topics being investigated by SCI faculty. These areas of computing are being applied to a wide variety of engineering applications ranging from fluid mechanics and solid mechanics to bioelectricity.


Martin Berzins

Parallel Computing

Mike Kirby

Finite Element Methods
Uncertainty Quantification

Valerio Pascucci

Scientific Data Management

Chris Johnson

Problem Solving Environments

Ross Whitaker


Chuck Hansen


Scientific Computing Project Sites:

Publications in Scientific Computing:

Finite Element Based Discretization and Regularization Strategies for 3D Inverse Electrocardiography
D. Wang, R.M. Kirby, C.R. Johnson. In IEEE Transactions for Biomedical Engineering, Vol. 58, No. 6, pp. 1827--1838. 2011.
PubMed ID: 21382763
PubMed Central ID: PMC3109267

We consider the inverse electrocardiographic problem of computing epicardial potentials from a body-surface potential map. We study how to improve numerical approximation of the inverse problem when the finite-element method is used. Being ill-posed, the inverse problem requires different discretization strategies from its corresponding forward problem. We propose refinement guidelines that specifically address the ill-posedness of the problem. The resulting guidelines necessitate the use of hybrid finite elements composed of tetrahedra and prism elements. Also, in order to maintain consistent numerical quality when the inverse problem is discretized into different scales, we propose a new family of regularizers using the variational principle underlying finite-element methods. These variational-formed regularizers serve as an alternative to the traditional Tikhonov regularizers, but preserves the L2 norm and thereby achieves consistent regularization in multiscale simulations. The variational formulation also enables a simple construction of the discrete gradient operator over irregular meshes, which is difficult to define in traditional discretization schemes. We validated our hybrid element technique and the variational regularizers by simulations on a realistic 3-D torso/heart model with empirical heart data. Results show that discretization based on our proposed strategies mitigates the ill-conditioning and improves the inverse solution, and that the variational formulation may benefit a broader range of potential-based bioelectric problems.

A Diffusion Approach to Network Localization
Y. Keller, Y. Gur. In IEEE Transactions on Signal Processing, Vol. 59, No. 6, pp. 2642--2654. 2011.
DOI: 10.1109/TSP.2011.2122261

Full-Resolution Interactive CPU Volume Rendering with Coherent BVH Traversal
A. Knoll, S. Thelen, I. Wald, C.D. Hansen, H. Hagen, M.E. Papka. In Proceedings of IEEE Pacific Visualization 2011, pp. 3--10. 2011.

From h to p Efficiently: Strategy Selection for Operator Evaluation on Hexahedral and Tetrahedral Elements
C.D. Cantwell, S.J. Sherwin, R.M. Kirby, P.H.J. Kelly. In Computers and Fluids, Vol. 43, No. 1, pp. 23--28. 2011.
DOI: 10.1016/j.compfluid.2010.08.012

Using Adjoint Error Estimation Techniques for Elastohydrodynamic Lubrication Line Contact Problems
D.E. Hart, M. Berzins, C.E. Goodyer, P.K. Jimack. In International Journal for Numerical Methods in Fluids, Vol. 67, Note: Published online 29 October, pp. 1559--1570. 2011.

Finite element modeling of subcutaneous implantable defibrillator electrodes in an adult torso
M. Jolley, J. Stinstra, J. Tate, S. Pieper, R.S. Macleod, L. Chu, P. Wang, J.K. Triedman. In Heart Rhythm, Vol. 7, No. 5, pp. 692--698. May, 2010.
DOI: 10.1016/j.hrthm.2010.01.030
PubMed ID: 20230927
PubMed Central ID: PMC3103844

Total subcutaneous implantable subcutaneous defibrillators are in development, but optimal electrode configurations are not known.

We used image-based finite element models (FEM) to predict the myocardial electric field generated during defibrillation shocks (pseudo-DFT) in a wide variety of reported and innovative subcutaneous electrode positions to determine factors affecting optimal lead positions for subcutaneous implantable cardioverter-defibrillators (S-ICD).

An image-based FEM of an adult man was used to predict pseudo-DFTs across a wide range of technically feasible S-ICD electrode placements. Generator location, lead location, length, geometry and orientation, and spatial relation of electrodes to ventricular mass were systematically varied. Best electrode configurations were determined, and spatial factors contributing to low pseudo-DFTs were identified using regression and general linear models.

A total of 122 single-electrode/array configurations and 28 dual-electrode configurations were simulated. Pseudo-DFTs for single-electrode orientations ranged from 0.60 to 16.0 (mean 2.65 +/- 2.48) times that predicted for the base case, an anterior-posterior configuration recently tested clinically. A total of 32 of 150 tested configurations (21%) had pseudo-DFT ratios /=1, indicating the possibility of multiple novel, efficient, and clinically relevant orientations. Favorable alignment of lead-generator vector with ventricular myocardium and increased lead length were the most important factors correlated with pseudo-DFT, accounting for 70% of the predicted variation (R(2) = 0.70, each factor P < .05) in a combined general linear modl in which parameter estimates were calculated for each factor.

Further exploration of novel and efficient electrode configurations may be of value in the development of the S-ICD technologies and implant procedure. FEM modeling suggests that the choice of configurations that maximize shock vector alignment with the center of myocardial mass and use of longer leads is more likely to result in lower DFT.

A New Family of Variational-Form-Based Regularizers for Reconstructing Epicardial Potentials from Body-Surface Mapping
D.F. Wang, R.M. Kirby, R.S. MacLeod, C.R. Johnson. In Computing in Cardiology, 2010, pp. 93--96. 2010.

h-p Efficiently: Implementing Finite and Spectral/hp Element Methods to Achieve Optimal Performance for Low- and High-Order Discretisations
P.E.J. Vos, S.J. Sherwin, R.M. Kirby. In Journal of Computational Physics, Vol. 229, No. 13, pp. 5161--5181. 2010.

Quantifying Variability in Radiation Dose Due to Respiratory-Induced Tumor Motion
S.E. Geneser, J.D. Hinkle, R.M. Kirby, Brian Wang, B. Salter, S. Joshi. In Medical Image Analysis, Vol. 15, No. 4, pp. 640--649. 2010.
DOI: 10.1016/

Towards the Development on an h-p-Refinement Strategy Based Upon Error Estimate Sensitivity
P.K. Jimack, R.M. Kirby. In Computers and Fluids, Vol. 46, No. 1, pp. 277--281. 2010.
DOI: 10.1016/j.compfluid.2010.08.003

The use of (a posteriori) error estimates is a fundamental tool in the application of adaptive numerical methods across a range of fluid flow problems. Such estimates are incomplete however, in that they do not necessarily indicate where to refine in order to achieve the most impact on the error, nor what type of refinement (for example h-refinement or p-refinement) will be best. This paper extends preliminary work of the authors (Comm Comp Phys, 2010;7:631–8), which uses adjoint-based sensitivity estimates in order to address these questions, to include application with p-refinement to arbitrary order and the use of practical a posteriori estimates. Results are presented which demonstrate that the proposed approach can guide both the h-refinement and the p-refinement processes, to yield improvements in the adaptive strategy compared to the use of more orthodox criteria.

Quantificiation of Errors Introduced in the Numerical Approximation and Implementation of Smoothness-Increasing Accuracy Conserving (SIAC) Filtering of Discontinuous Galerkin (DG) Fields
H. Mirzaee, J.K. Ryan, R.M. Kirby. In Journal of Scientific Computing, Vol. 45, pp. 447-470. 2010.

Resolution Strategies for the Finite-Element-Based Solution of the ECG Inverse Problem
D.F. Wang, R.M. Kirby, C.R. Johnson. In IEEE Transactions on Biomedical Engineering, Vol. 57, No. 2, pp. 220--237. February, 2010.

Decoupling and Balancing of Space and Time Errors in the Material Point Method (MPM)
M. Steffen, R.M. Kirby, M. Berzins. In International Journal for Numerical Methods in Engineering, Vol. 82, No. 10, pp. 1207--1243. 2010.

Scientific Grand Challenges: Opportunities in biology at the Extreme Scale of Computing
M. Ellisman, R. Stevens, M. Colvin, T. Schlick, E. Delong, G. Olsen, J. George, G. Karniakadis, C.R. Johnson, N. Sematova. Note: DOE Office of Advanced Scientific Computing Research, August, 2009.

Incorporating patient breathing variability into a stochastic model of dose deposition for stereotactic body radiation therapy
S.E. Geneser, R.M. Kirby, Brian Wang, B. Salter, S. Joshi. In Information Processing in Medical Imaging, Lecture Notes in Computer Science LNCS, Vol. 5636, pp. 688--700. 2009.
PubMed ID: 19694304

Finite Element Discretization Strategies for the Inverse Electrocardiographic (ECG) Problem
D.F. Wang, R.M. Kirby, C.R. Johnson. In Proceedings of the 11th World Congress on Medical Physics and Biomedical Engineering, Munich, Germany, Vol. 25/2, pp. 729-732. September, 2009.

Finite Element Refinements for Inverse Electrocardiography: Hybrid-Shaped Elements, High-Order Element Truncation and Variational Gradient Operator
D.F. Wang, R.M. Kirby, C.R. Johnson. In Proceeding of Computers in Cardiology 2009, Park City, September, 2009.

A Framework for Exploring Numerical Solutions of Advection Reaction Diffusion Equations using a GPU Based Approach
A.R. Sanderson, M.D. Meyer, R.M. Kirby, C.R. Johnson. In Journal of Computing and Visualization in Science, Vol. 12, pp. 155--170. 2009.
DOI: 10.1007/s00791-008-0086-0

Subject-specific, multiscale simulation of electrophysiology: a software pipeline for image-based models and application examples
R.S. MacLeod, J.G. Stinstra, S. Lew, R.T. Whitaker, D.J. Swenson, M.J. Cole, J. Krüger, D.H. Brooks, C.R. Johnson. In Philosophical Transactions of The Royal Society A, Mathematical, Physical & Engineering Sciences, Vol. 367, No. 1896, pp. 2293--2310. 2009.

Hexahedral Mesh Generation for Biomedical Models in SCIRun
J.F. Shepherd, C.R. Johnson. In Engineering with Computers, Vol. 25, No. 1, pp. 97--114. 2009.